1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with Eigenvalues problem

  1. Jul 21, 2009 #1
    1. The problem statement, all variables and given/known data

    True/False

    If Ttheta is a rotation of the Euclidean plane R2 counterclockwise through an angle theta, then T can be represented by an orthogonal matrix P whose eigenvalues are lambda1 = 1 and lambda2 = -1.

    2. Relevant equations



    3. The attempt at a solution

    Just checking to see if my thinking is right. I say false because the representation of T in orthogonal coordinates would require a transformation requiring trigonometric functions. This wouldn't be a linear transformation and therefore cannot be treated as an eigensystem.

    Yes? No?
     
  2. jcsd
  3. Jul 21, 2009 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: Eigenvalues

    The answer is false, but I can't figure out what you're trying to say for your reasoning. Rotations are linear functions of the plane, and can be represented my matrices. You can either consider determinants, or try to demonstrate no rotation can do what is proposed to the two eigenvectors
     
  4. Jul 21, 2009 #3

    Pengwuino

    User Avatar
    Gold Member

    Re: Eigenvalues

    Using sines and cosines is still a linear transformation.

    Think of it this way, what is the determinant of a matrix such that it's eigenvalues are -1,1?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Help with Eigenvalues problem
  1. Eigenvalue Problem (Replies: 3)

  2. Eigenvalue problem. (Replies: 3)

Loading...